Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you find a way to identify times tables after they have been shifted up or down?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Can you figure out how sequences of beach huts are generated?

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Can you find the connections between linear and quadratic patterns?

What do you notice about the sum of two identical triangular numbers?